Start with a sex-mad baroness and her frisky menage a trois. Add in a stern German philosopher who fancied himself the next Friedriche Nietzsche, his mistress and a married couple who wanted a wholesome Swiss Family Robinson experience for their son. Throw them all together on one of the remotest spots on Earth and simmer until things come to a steamy boil.

You couldn’t make this stuff up, and, as a lively new documentary reports, you don’t have to.

“The Galapagos Affair: Satan Came to Eden” tells a humdinger of a story about wild doings on those celebrated islands off the coast of Ecuador. As directed by Danya Goldfine and Dan Geller, this captivating tale is pure pulp fiction that has the advantage of actually having happened.

It was 1998 when Goldfine and Geller, whose documentaries include the excellent “Ballets Russes,” stumbled on this 1930s story, a tale much told back in the day, with men’s magazines running stories with headlines like “The Insatiable Baroness Who Created a Private Paradise.”

But given that its key participants are all dead, the duo struggled for years with the specifics of how to turn it into a film before a number of factors combined to create a splendid solution.

Most important, the filmmakers stumbled upon an archive of actual footage of all the key players that had been deposited at the University of Southern California. Second, helped by casting director Margery Simkin, they recruited a wealth of first-class voice talent, including Cate Blanchett, Diane Kruger and Connie Nielsen, to read the actual words of the participants.

Next, extensive on-camera interviewing was done with descendants of the key players and the old-time Galapagos settlers, the better to place the story in context. Finally, ace editor Bill Weber (“We Were Here,” “The Cockettes”) was employed to make all this footage flow smoothly together.

No one was more surprised that this story had such a tempestuous resolution than the participants themselves. As Dore Strauch (voiced by Blanchett) wrote in 1934, “life can make a poor end of fine and admirable beginnings. Five years ago we came to make an Eden on these shores. We could not have foreseen the strange and sinister drama that has been unleashed.”

Strauch and her lover Friedrich Ritter (voiced by Thomas Kretschmann) were the original inhabitants of Floreana, one of the Galapagos, deserting spouses in Germany and arriving in 1929. “We are turning our backs on civilization,” wrote the doctor, a believer in the power of discipline who spent so much time writing dense philosophical tomes that Strauch inevitably felt neglected.

Unknown to these two, their letters home had been leaked to German newspapers, where they were celebrated as “a modern Adam and Eve,” leading to visitors they were not happy about.

First to arrive was Allan Hancock, a wealthy Southern Californian with an interest in scientific expeditions, who showed up on a research vessel. Then and in succeeding trips, he took the hours of footage that are the heart of this film’s visuals.

The next set, who came not to visit but to stay, were Margaret and Heinz Wittmer, who arrived to provide a healthy lifestyle for their son Harry. Much less bohemian than Ritter and Strauch, they were given the “this island isn’t big enough for both of us” treatment by the original settlers.

The last group, who made absolutely everybody crazy, was the Baroness Eloise von Wagner (voiced by Nielsen), who showed up with her two male lovers (“servile gigolos,” harrumphed Ritter) and a vague determination to start a luxury hotel for the hordes of wealthy yachtsmen she was sure were headed in their direction.

Though the other women were especially upset at her presence (“a woman whose love of sensation will stop at nothing,” said Margaret Wittmer), the baroness had no doubt about her own charms.

“The man isn’t born who can resist me,” she wrote. “I find variety to be the spice of life.” Among those infatuated was businessman Hancock, who bankrolled a dreadful silent film called “The Empress of Floreana,” which featured the baroness as a pirate queen whose life force practically jumps off the screen.

Though it’s clear that a film with the subtitle “Satan Came to Eden” will not have a cheerful conclusion, directors Goldfine and Geller tell their story with such engaged confidence that we are swept along to its wild end. Move over, Charles Darwin, when it comes to great tales about the Galapagos, you’ve got company.

‘THE GALAPAGOS AFFAIR: SATAN CAME TO EDEN’

Directed by: Danya Goldfine and Dan Geller

Starring: Voiced by Cate Blanchett, Diane Kruger and Connie Nielsen

Rated: Unrated.

Should you go? It’s strange but true. ***

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